The cycle of cell growth, DNA synthesis, mitosis and cell division is fundamental process by which cells (and all living organisms) grow, develop and reproduce. Hence, it is of crucial importance to science and human health to understand the molecular mechanisms that control these processes in eukaryotic cells. The control system is so complex that mathematical and computational methods are needed to reliably track the interactions of dozens of genes, mRNAs, proteins, and multiprotein complexes. Deterministic models (ordinary differential equations) are adequate for understanding the average behavior of groups of cells, but to understand the far-from-average behavior of individual cells requires stochastic models that accurately account for noisy events in the growth-division cycle. Noise stems from small numbers of participating molecules within a single cell, and from vagaries of the division process (i.e., unequal partitioning of molecular components between daughter cells). The goal of the proposed project is to create a realistic and accurate stochastic model of cell cycle control in budding yeast. To accomplish this goal the investigators will: 1) Formulate the molecular regulatory system in terms of elementary biochemical reactions, suitable for exact stochastic simulation. 2) Employ appropriate methods for approximate simulation of these stochastic process, in order to efficiently compute probabilities suitable for comparison to experiments. 3) Develop methods for parameter estimation, sensitivity analysis and bifurcation theory of stochastic dynamical systems. 4) Create a software/hardware environment that supports the demanding computations required of stochastic models of any realistic gene/mRNA/protein regulatory network. 5) Apply the methods and tools to known variability in growth and division of single yeast cells. The multi-disciplinary team at Virginia Tech has proven expertise in all aspects of the project and will be supported by external advisors who are top researchers in the areas of stochastic simulation, sensitivity analysis, bifurcation theory and yeast genetics. Because all eukaryotic cells seem to employ the same fundamental molecular machinery that regulates the cell cycle of yeast, success in modeling growth and division of single yeast cells will translate into better understanding of the roles of cell division in basic biological processes of significant relevance to human health: e.g., embyronic development, tissue regeneration, wound healing, and carcinogenesis.